Setting the amount of a child support award involves tradeoffs in the allocation of finite resources among at least three private parties: the two parents, and their child or children. Federal law today requires states to have child support guidelines or formulas that determine child support amounts on a uniform statewide basis. These state guidelines differ in how they make these unavoidable tradeoffs. In choosing the correct balance of these competing claims, policymakers would do well to understand the public's intuitions about the appropriate tradeoffs. We report an empirical study of lay intuitions about these tradeoffs, which we compare to the principles underlying typical state guidelines. As in other contexts in which people are asked to place a dollar value on a legal claim, we find that citizen assessments of child support for particular cases conform to the pattern that Ariely and his co-authors have called “coherent arbitrariness”: the respondent's choice of dollar magnitude may be arbitrary, but relative values respond coherently to case variations, within and across citizens. These patterns also suggest that our respondents have a consistent and systematic preference with respect to the structure of child support formulas that differs in important ways from either of the two systems adopted by nearly all states.